In this work we show that the optimal digital communication strategy for transmissions over time-varying channels with spread function maximally concentrated along a line of the delay-Doppler domain consists in multiplexing the input symbol block with an IFFT, as in OFDM, and modulating the IFFT output with a chirp signal whose sweep rate is matched to the channel. We show how to allocate the transmit power optimally across the chirped subcarriers, derive the limits of applicability of the proposed chirped-OFDM scheme and compute the resulting BER curves